SOLUTION: 1) x^2/(x-3)=(x+2)/(2x-5) 2) (1/x)<[1/(x-3)] Please help me... Thank you!

Question 1187209: 1) x^2/(x-3)=(x+2)/(2x-5)
2) (1/x)<[1/(x-3)]
Please help me... Thank you!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1) x^2/(x-3)=(x+2)/(2x-5)
x^2*(2x-5) = (x-3)*(x+2)
2x^3 - 5x^2 = x^2 - x - 6
2x^3 - 6x^2 + x + 6 = 0
2 is a zero, divide by (x-2)
(2x^3 - 6x^2 + x + 6)/(x-2) = 2x^2 - 2x - 3 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=28 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.8228756555323, -0.822875655532295. Here's your graph:

2) (1/x)<[1/(x-3)]
multiply by x(x-3)
---
x-3 < x
-3 < 0
x <> 0 and x <> 3 ---> zero in a denominator
-----
x is any other number
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